[R] lme and aov
Peter Dalgaard
p.dalgaard at biostat.ku.dk
Fri Aug 3 22:53:43 CEST 2007
Gang Chen wrote:
> Thanks a lot for clarification! I just started to learn programming in
> R for a week, and wanted to try a simple mixed design of balanced
> ANOVA with a between-subject factor
> (Grp) and a within-subject factor (Rsp), but I'm not sure whether I'm
> modeling the data correctly with either of the command lines.
>
> Here is the result. Any help would be highly appreciated.
>
> > fit.lme <- lme(Beta ~ Grp*Rsp, random = ~1|Subj, Model);
> > summary(fit.lme)
> Linear mixed-effects model fit by REML
> Data: Model
> AIC BIC logLik
> 233.732 251.9454 -108.8660
>
> Random effects:
> Formula: ~1 | Subj
> (Intercept) Residual
> StdDev: 1.800246 0.3779612
>
> Fixed effects: Beta ~ Grp * Rsp
> Value Std.Error DF t-value p-value
> (Intercept) 1.1551502 0.5101839 36 2.2641837 0.0297
> GrpB -1.1561248 0.7215090 36 -1.6023706 0.1178
> GrpC -1.2345321 0.7215090 36 -1.7110417 0.0957
> RspB -0.0563077 0.1482486 36 -0.3798196 0.7063
> GrpB:RspB -0.3739339 0.2096551 36 -1.7835665 0.0829
> GrpC:RspB 0.3452539 0.2096551 36 1.6467705 0.1083
> Correlation:
> (Intr) GrpB GrpC RspB GrB:RB
> GrpB -0.707
> GrpC -0.707 0.500
> RspB -0.145 0.103 0.103
> GrpB:RspB 0.103 -0.145 -0.073 -0.707
> GrpC:RspB 0.103 -0.073 -0.145 -0.707 0.500
>
> Standardized Within-Group Residuals:
> Min Q1 Med Q3 Max
> -1.72266114 -0.41242552 0.02994094 0.41348767 1.72323563
>
> Number of Observations: 78
> Number of Groups: 39
>
> > fit.aov <- aov(Beta ~ Rsp*Grp+Error(Subj/Rsp)+Grp, Model);
> > fit.aov
>
> Call:
> aov(formula = Beta ~ Rsp * Grp + Error(Subj/Rsp) + Grp, data = Model)
>
> Grand Mean: 0.3253307
>
> Stratum 1: Subj
>
> Terms:
> Grp
> Sum of Squares 5.191404
> Deg. of Freedom 1
>
> 1 out of 2 effects not estimable
> Estimated effects are balanced
>
> Stratum 2: Subj:Rsp
>
> Terms:
> Rsp
> Sum of Squares 7.060585e-05
> Deg. of Freedom 1
>
> 2 out of 3 effects not estimable
> Estimated effects are balanced
>
> Stratum 3: Within
>
> Terms:
> Rsp Grp Rsp:Grp Residuals
> Sum of Squares 0.33428 36.96518 1.50105 227.49594
> Deg. of Freedom 1 2 2 70
>
> Residual standard error: 1.802760
> Estimated effects may be unbalanced
>
This looks odd. It is a standard split-plot layout, right? 3 groups of
13 subjects, each measured with two kinds of Rsp = 3x13x2 = 78
observations.
In that case you shouldn't see the same effect allocated to multiple
error strata. I suspect you forgot to declare Subj as factor.
Also: summary(fit.aov) is nicer, and anova(fit.lme) should be informative.
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